1. Find the number of factors of 64.
a. 2
b. 5
c. 7
d. 9
Answer: C
Explanation:
We know that $64 = {2^6}$
So number of factors of $64 =$ $1,\;2,\;{2^2},\;{2^3},\;{2^4},\;{2^5},\;{2^6}$.
Total factors are 7.
2. Find the number of factors of 64 which are even.
a. 6
b. 7
c. 4
d. 3
Answer: A
Explanation:
We know that $64 = {2^6}$
Number of factors of $64 =$ $1,\;2,\;{2^2},\;{2^3},\;{2^4},\;{2^5},\;{2^6}$.
Except 1, all remaining factors are even.
$\therefore$ Even factors are 6.
3. Find the number of factors of 64 which are perfect squares
a. 4
b. 5
c. 6
d. 7
Answer: A
Explanation:
We know that $64 = {2^6}$
Perfect square factors have their powers even.
So the number of perfect square factors of $64$ are $1,\;{2^2},\;{2^4},\;{2^6}$.
$\therefore$ Perfect square factors are 4.
4. Find the number of factors of 64 which are perfect cubes.
a. 6
b. 9
c. 4
d. 3
Answer: D
Explanation:
We know that $64 = {2^6}$
Perfect cube factors have their powers multiples of 3.
So the number of perfect square factors of $64$ are $1,\;{2^3},\;{2^6}$.
$\therefore$ perfect cube factors are 3.
5. How many numbers below 100 have exactly 2 factors.
a. 25
b. 10
c. 17
d. 18
Answer: A
Explanation:
Only prime numbers have exactly two factors or divisors. i.e., Which are divisible by 1 and the number itself.
So total primes are 25.
6. How many factors of 81 are odd.
a. 4
b. 5
c. 1
d. 2
Answer: C
Explanation:
The prime factorization of 81 = ${3^4}$
The number of factors are = $1,\,3,\,{3^2},\,{3^3},\,{3^4}$
All factors are odd numbers.
